Infinite triangular hyperbolic tilings | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(p q r) | t0 | h0 | t01 | h01 | t1 | h1 | t12 | h12 | t2 | h2 | t02 | h02 | t012 | s | |||||
(∞ 3 2) |
t0{∞,3} ∞3 |
h0{∞,3} (3.∞)3 |
t01{∞,3} ∞.3.∞ |
t1{∞,3} (3.∞)2 |
t12{∞,3} 6.∞.6 |
h12{∞,3} 3.3.3.∞.3.3 |
t2{∞,3} 3∞ |
t02{∞,3} 3.4.∞.4 |
t012{∞,3} 4.6.∞ |
s{∞,3} 3.3.3.3.∞ | |||||||||
(∞ 4 2) |
t0{∞,4} ∞4 |
h0{∞,4} (4.∞)4 |
t01{∞,4} ∞.4.∞ |
h01{∞,4} 3.∞.3.3.∞ |
t1{∞,4} (4.∞)2 |
h1{∞,4} (4.4.∞)2 |
t12{∞,4} 8.∞.8 |
h12{∞,4} 3.4.3.∞.3.4 |
t2{∞,4} 4∞ |
h2{∞,4} ∞∞ |
t02{∞,4} 4.4.∞.4 |
h02{∞,4} 4.4.4.∞.4 |
t012{∞,4} 4.8.∞ |
s{∞,4} 3.3.4.3.∞ | |||||
(∞ 5 2) |
t0{∞,5} ∞5 |
h0{∞,5} (5.∞)5 |
t01{∞,5} ∞.5.∞ |
t1{∞,5} (5.∞)2 |
t12{∞,5} 10.∞.10 |
h12{∞,5} 3.5.3.∞.3.5 |
t2{∞,5} 5∞ |
t02{∞,5} 5.4.∞.4 |
t012{∞,5} 4.10.∞ |
s{∞,5} 3.3.5.3.∞ | |||||||||
(∞ 6 2) |
t0{∞,6} ∞6 |
h0{∞,6} (6.∞)6 |
t01{∞,6} ∞.6.∞ |
h01{∞,6} 3.∞.3.3.3.∞ |
t1{∞,6} (6.∞)2 |
h1{∞,6} (4.3.4.∞)2 |
t12{∞,6} 12.∞.12 |
h12{∞,6} 3.6.3.∞.3.6 |
t2{∞,6} 6∞ |
h2{∞,6} (∞.3)∞ |
t02{∞,6} 6.4.∞.4 |
h02{∞,6} 4.3.4.4.∞.4 |
t012{∞,6} 4.12.∞ |
s{∞,6} 3.3.6.3.∞ | |||||
(∞ 7 2) |
t0{∞,7} ∞7 |
h0{∞,7} (7.∞)7 |
t01{∞,7} ∞.7.∞ |
t1{∞,7} (7.∞)2 |
t12{∞,7} 14.∞.14 |
h12{∞,7} 3.7.3.∞.3.7 |
t2{∞,7} 7∞ |
t02{∞,7} 7.4.∞.4 |
t012{∞,7} 4.14.∞ |
s{∞,7} 3.3.7.3.∞ | |||||||||
(∞ 8 2) |
t0{∞,8} ∞8 |
h0{∞,8} (8.∞)8 |
t01{∞,8} ∞.8.∞ |
h01{∞,8} 3.∞.3.4.3.∞ |
t1{∞,8} (8.∞)2 |
h1{∞,8} (4.4.4.∞)2 |
t12{∞,8} 16.∞.16 |
h12{∞,8} 3.8.3.∞.3.8 |
t2{∞,8} 8∞ |
h2{∞,8} (∞.4)∞ |
t02{∞,8} 8.4.∞.4 |
h02{∞,8} 4.4.4.4.∞.4 |
t012{∞,8} 4.16.∞ |
s{∞,8} 3.3.8.3.∞ | |||||
(∞ ∞ 2) |
t0{∞,∞} ∞∞ |
h0{∞,∞} (∞.∞)∞ |
t01{∞,∞} ∞.∞.∞ |
h01{∞,∞} 3.∞.3.∞.3.∞ |
t1{∞,∞} ∞4 |
h1{∞,∞} (4.∞)4 |
t12{∞,∞} ∞.∞.∞ |
h12{∞,∞} 3.∞.3.∞.3.∞ |
t2{∞,∞} ∞∞ |
h2{∞,∞} (∞.∞)∞ |
t02{∞,∞} (∞.4)2 |
h02{∞,∞} (4.∞.4)2 |
t012{∞,∞} 4.∞.∞ |
s{∞,∞} 3.3.∞.3.∞ | |||||
(∞ 3 3) |
t0(∞,3,3) (∞.3)3 |
t01(∞,3,3) (3.∞)2 |
t1(∞,3,3) (3.∞)3 |
t12(∞,3,3) 3.6.∞.6 |
t2(∞,3,3) 3∞ |
t02(∞,3,3) 3.6.∞.6 |
t012(∞,3,3) 6.6.∞ |
s(∞,3,3) 3.3.3.3.3.∞ | |||||||||||
(∞ 4 3) |
t0(∞,4,3) (∞.3)4 |
t01(∞,4,3) 3.∞.4.∞ |
t1(∞,4,3) (4.∞)3 |
h1(∞,4,3) (6.6.∞)3 |
t12(∞,4,3) 3.8.∞.8 |
t2(∞,4,3) (4.3)∞ |
t02(∞,4,3) 4.6.∞.6 |
h02(∞,4,3) 4.4.3.4.∞.4.3 |
t012(∞,4,3) 6.8.∞ |
s(∞,4,3) 3.3.3.4.3.∞ | |||||||||
(∞ 5 3) |
t0(∞,5,3) (∞.3)5 |
t01(∞,5,3) 3.∞.5.∞ |
t1(∞,5,3) (5.∞)3 |
t12(∞,5,3) 3.10.∞.10 |
t2(∞,5,3) (5.3)∞ |
t02(∞,5,3) 5.6.∞.6 |
t012(∞,5,3) 6.10.∞ |
s(∞,5,3) 3.3.3.5.3.∞ | |||||||||||
(∞ 6 3) |
t0(∞,6,3) (∞.3)6 |
t01(∞,6,3) 3.∞.6.∞ |
t1(∞,6,3) (6.∞)3 |
h1(∞,6,3) (6.3.6.∞)3 |
t12(∞,6,3) 3.12.∞.12 |
t2(∞,6,3) (6.3)∞ |
t02(∞,6,3) 6.6.∞.6 |
h02(∞,6,3) 4.3.4.3.4.∞.4.3 |
t012(∞,6,3) 6.12.∞ |
s(∞,6,3) 3.3.3.6.3.∞ | |||||||||
(∞ 7 3) |
t0(∞,7,3) (∞.3)7 |
t01(∞,7,3) 3.∞.7.∞ |
t1(∞,7,3) (7.∞)3 |
t12(∞,7,3) 3.14.∞.14 |
t2(∞,7,3) (7.3)∞ |
t02(∞,7,3) 7.6.∞.6 |
t012(∞,7,3) 6.14.∞ |
s(∞,7,3) 3.3.3.7.3.∞ | |||||||||||
(∞ 8 3) |
t0(∞,8,3) (∞.3)8 |
t01(∞,8,3) 3.∞.8.∞ |
t1(∞,8,3) (8.∞)3 |
h1(∞,8,3) (6.4.6.∞)3 |
t12(∞,8,3) 3.16.∞.16 |
t2(∞,8,3) (8.3)∞ |
t02(∞,8,3) 8.6.∞.6 |
h02(∞,8,3) 4.4.4.3.4.∞.4.3 |
t012(∞,8,3) 6.16.∞ |
s(∞,8,3) 3.3.3.8.3.∞ | |||||||||
(∞ ∞ 3) |
t0(∞,∞,3) (∞.3)∞ |
t01(∞,∞,3) 3.∞.∞.∞ |
t1(∞,∞,3) ∞6 |
h1(∞,∞,3) (6.∞)6 |
t12(∞,∞,3) 3.∞.∞.∞ |
t2(∞,∞,3) (∞.3)∞ |
t02(∞,∞,3) (∞.6)2 |
h02(∞,∞,3) (4.∞.4.3)2 |
t012(∞,∞,3) 6.∞.∞ |
s(∞,∞,3) 3.3.3.∞.3.∞ | |||||||||
(∞ 4 4) |
t0(∞,4,4) (∞.4)4 |
h0(∞,4,4) (8.∞.8)4 |
t01(∞,4,4) (4.∞)2 |
h01(∞,4,4) (4.4.∞)2 |
t1(∞,4,4) (4.∞)4 |
h1(∞,4,4) (8.8.∞)4 |
t12(∞,4,4) 4.8.∞.8 |
h12(∞,4,4) 4.4.4.4.∞.4.4 |
t2(∞,4,4) 4∞ |
h2(∞,4,4) ∞∞ |
t02(∞,4,4) 4.8.∞.8 |
h02(∞,4,4) 4.4.4.4.∞.4.4 |
t012(∞,4,4) 8.8.∞ |
s(∞,4,4) 3.4.3.4.3.∞ | |||||
(∞ 5 4) |
t0(∞,5,4) (∞.4)5 |
h0(∞,5,4) (10.∞.10)5 |
t01(∞,5,4) 4.∞.5.∞ |
t1(∞,5,4) (5.∞)4 |
t12(∞,5,4) 4.10.∞.10 |
h12(∞,5,4) 4.4.5.4.∞.4.5 |
t2(∞,5,4) (5.4)∞ |
t02(∞,5,4) 5.8.∞.8 |
t012(∞,5,4) 8.10.∞ |
s(∞,5,4) 3.4.3.5.3.∞ | |||||||||
(∞ 6 4) |
t0(∞,6,4) (∞.4)6 |
h0(∞,6,4) (12.∞.12)6 |
t01(∞,6,4) 4.∞.6.∞ |
h01(∞,6,4) 4.4.∞.4.3.4.∞ |
t1(∞,6,4) (6.∞)4 |
h1(∞,6,4) (8.3.8.∞)4 |
t12(∞,6,4) 4.12.∞.12 |
h12(∞,6,4) 4.4.6.4.∞.4.6 |
t2(∞,6,4) (6.4)∞ |
h2(∞,6,4) (∞.3.∞)∞ |
t02(∞,6,4) 6.8.∞.8 |
h02(∞,6,4) 4.3.4.4.4.∞.4.4 |
t012(∞,6,4) 8.12.∞ |
s(∞,6,4) 3.4.3.6.3.∞ | |||||
(∞ 7 4) |
t0(∞,7,4) (∞.4)7 |
h0(∞,7,4) (14.∞.14)7 |
t01(∞,7,4) 4.∞.7.∞ |
t1(∞,7,4) (7.∞)4 |
t12(∞,7,4) 4.14.∞.14 |
h12(∞,7,4) 4.4.7.4.∞.4.7 |
t2(∞,7,4) (7.4)∞ |
t02(∞,7,4) 7.8.∞.8 |
t012(∞,7,4) 8.14.∞ |
s(∞,7,4) 3.4.3.7.3.∞ | |||||||||
(∞ 8 4) |
t0(∞,8,4) (∞.4)8 |
h0(∞,8,4) (16.∞.16)8 |
t01(∞,8,4) 4.∞.8.∞ |
h01(∞,8,4) 4.4.∞.4.4.4.∞ |
t1(∞,8,4) (8.∞)4 |
h1(∞,8,4) (8.4.8.∞)4 |
t12(∞,8,4) 4.16.∞.16 |
h12(∞,8,4) 4.4.8.4.∞.4.8 |
t2(∞,8,4) (8.4)∞ |
h2(∞,8,4) (∞.4.∞)∞ |
t02(∞,8,4) 8.8.∞.8 |
h02(∞,8,4) 4.4.4.4.4.∞.4.4 |
t012(∞,8,4) 8.16.∞ |
s(∞,8,4) 3.4.3.8.3.∞ | |||||
(∞ ∞ 4) |
t0(∞,∞,4) (∞.4)∞ |
h0(∞,∞,4) (∞.∞.∞)∞ |
t01(∞,∞,4) 4.∞.∞.∞ |
h01(∞,∞,4) 4.4.∞.4.∞.4.∞ |
t1(∞,∞,4) ∞8 |
h1(∞,∞,4) (8.∞)8 |
t12(∞,∞,4) 4.∞.∞.∞ |
h12(∞,∞,4) 4.4.∞.4.∞.4.∞ |
t2(∞,∞,4) (∞.4)∞ |
h2(∞,∞,4) (∞.∞.∞)∞ |
t02(∞,∞,4) (∞.8)2 |
h02(∞,∞,4) (4.∞.4.4)2 |
t012(∞,∞,4) 8.∞.∞ |
s(∞,∞,4) 3.4.3.∞.3.∞ | |||||
(∞ 5 5) |
t0(∞,5,5) (∞.5)5 |
t01(∞,5,5) (5.∞)2 |
t1(∞,5,5) (5.∞)5 |
t12(∞,5,5) 5.10.∞.10 |
t2(∞,5,5) 5∞ |
t02(∞,5,5) 5.10.∞.10 |
t012(∞,5,5) 10.10.∞ |
s(∞,5,5) 3.5.3.5.3.∞ | |||||||||||
(∞ 6 5) |
t0(∞,6,5) (∞.5)6 |
t01(∞,6,5) 5.∞.6.∞ |
t1(∞,6,5) (6.∞)5 |
h1(∞,6,5) (10.3.10.∞)5 |
t12(∞,6,5) 5.12.∞.12 |
t2(∞,6,5) (6.5)∞ |
t02(∞,6,5) 6.10.∞.10 |
h02(∞,6,5) 4.3.4.5.4.∞.4.5 |
t012(∞,6,5) 10.12.∞ |
s(∞,6,5) 3.5.3.6.3.∞ | |||||||||
(∞ 7 5) |
t0(∞,7,5) (∞.5)7 |
t01(∞,7,5) 5.∞.7.∞ |
t1(∞,7,5) (7.∞)5 |
t12(∞,7,5) 5.14.∞.14 |
t2(∞,7,5) (7.5)∞ |
t02(∞,7,5) 7.10.∞.10 |
t012(∞,7,5) 10.14.∞ |
s(∞,7,5) 3.5.3.7.3.∞ | |||||||||||
(∞ 8 5) |
t0(∞,8,5) (∞.5)8 |
t01(∞,8,5) 5.∞.8.∞ |
t1(∞,8,5) (8.∞)5 |
h1(∞,8,5) (10.4.10.∞)5 |
t12(∞,8,5) 5.16.∞.16 |
t2(∞,8,5) (8.5)∞ |
t02(∞,8,5) 8.10.∞.10 |
h02(∞,8,5) 4.4.4.5.4.∞.4.5 |
t012(∞,8,5) 10.16.∞ |
s(∞,8,5) 3.5.3.8.3.∞ | |||||||||
(∞ ∞ 5) |
t0(∞,∞,5) (∞.5)∞ |
t01(∞,∞,5) 5.∞.∞.∞ |
t1(∞,∞,5) ∞10 |
h1(∞,∞,5) (10.∞)10 |
t12(∞,∞,5) 5.∞.∞.∞ |
t2(∞,∞,5) (∞.5)∞ |
t02(∞,∞,5) (∞.10)2 |
h02(∞,∞,5) (4.∞.4.5)2 |
t012(∞,∞,5) 10.∞.∞ |
s(∞,∞,5) 3.5.3.∞.3.∞ | |||||||||
(∞ 6 6) |
t0(∞,6,6) (∞.6)6 |
h0(∞,6,6) (12.∞.12.3)6 |
t01(∞,6,6) (6.∞)2 |
h01(∞,6,6) (4.3.4.∞)2 |
t1(∞,6,6) (6.∞)6 |
h1(∞,6,6) (12.3.12.∞)6 |
t12(∞,6,6) 6.12.∞.12 |
h12(∞,6,6) 4.3.4.6.4.∞.4.6 |
t2(∞,6,6) 6∞ |
h2(∞,6,6) (∞.3)∞ |
t02(∞,6,6) 6.12.∞.12 |
h02(∞,6,6) 4.3.4.6.4.∞.4.6 |
t012(∞,6,6) 12.12.∞ |
s(∞,6,6) 3.6.3.6.3.∞ | |||||
(∞ 7 6) |
t0(∞,7,6) (∞.6)7 |
h0(∞,7,6) (14.∞.14.3)7 |
t01(∞,7,6) 6.∞.7.∞ |
t1(∞,7,6) (7.∞)6 |
t12(∞,7,6) 6.14.∞.14 |
h12(∞,7,6) 4.3.4.7.4.∞.4.7 |
t2(∞,7,6) (7.6)∞ |
t02(∞,7,6) 7.12.∞.12 |
t012(∞,7,6) 12.14.∞ |
s(∞,7,6) 3.6.3.7.3.∞ | |||||||||
(∞ 8 6) |
t0(∞,8,6) (∞.6)8 |
h0(∞,8,6) (16.∞.16.3)8 |
t01(∞,8,6) 6.∞.8.∞ |
h01(∞,8,6) 4.3.4.∞.4.4.4.∞ |
t1(∞,8,6) (8.∞)6 |
h1(∞,8,6) (12.4.12.∞)6 |
t12(∞,8,6) 6.16.∞.16 |
h12(∞,8,6) 4.3.4.8.4.∞.4.8 |
t2(∞,8,6) (8.6)∞ |
h2(∞,8,6) (∞.4.∞.3)∞ |
t02(∞,8,6) 8.12.∞.12 |
h02(∞,8,6) 4.4.4.6.4.∞.4.6 |
t012(∞,8,6) 12.16.∞ |
s(∞,8,6) 3.6.3.8.3.∞ | |||||
(∞ ∞ 6) |
t0(∞,∞,6) (∞.6)∞ |
h0(∞,∞,6) (∞.∞.∞.3)∞ |
t01(∞,∞,6) 6.∞.∞.∞ |
h01(∞,∞,6) 4.3.4.∞.4.∞.4.∞ |
t1(∞,∞,6) ∞12 |
h1(∞,∞,6) (12.∞)12 |
t12(∞,∞,6) 6.∞.∞.∞ |
h12(∞,∞,6) 4.3.4.∞.4.∞.4.∞ |
t2(∞,∞,6) (∞.6)∞ |
h2(∞,∞,6) (∞.∞.∞.3)∞ |
t02(∞,∞,6) (∞.12)2 |
h02(∞,∞,6) (4.∞.4.6)2 |
t012(∞,∞,6) 12.∞.∞ |
s(∞,∞,6) 3.6.3.∞.3.∞ | |||||
(∞ 7 7) |
t0(∞,7,7) (∞.7)7 |
t01(∞,7,7) (7.∞)2 |
t1(∞,7,7) (7.∞)7 |
t12(∞,7,7) 7.14.∞.14 |
t2(∞,7,7) 7∞ |
t02(∞,7,7) 7.14.∞.14 |
t012(∞,7,7) 14.14.∞ |
s(∞,7,7) 3.7.3.7.3.∞ | |||||||||||
(∞ 8 7) |
t0(∞,8,7) (∞.7)8 |
t01(∞,8,7) 7.∞.8.∞ |
t1(∞,8,7) (8.∞)7 |
h1(∞,8,7) (14.4.14.∞)7 |
t12(∞,8,7) 7.16.∞.16 |
t2(∞,8,7) (8.7)∞ |
t02(∞,8,7) 8.14.∞.14 |
h02(∞,8,7) 4.4.4.7.4.∞.4.7 |
t012(∞,8,7) 14.16.∞ |
s(∞,8,7) 3.7.3.8.3.∞ | |||||||||
(∞ ∞ 7) |
t0(∞,∞,7) (∞.7)∞ |
t01(∞,∞,7) 7.∞.∞.∞ |
t1(∞,∞,7) ∞14 |
h1(∞,∞,7) (14.∞)14 |
t12(∞,∞,7) 7.∞.∞.∞ |
t2(∞,∞,7) (∞.7)∞ |
t02(∞,∞,7) (∞.14)2 |
h02(∞,∞,7) (4.∞.4.7)2 |
t012(∞,∞,7) 14.∞.∞ |
s(∞,∞,7) 3.7.3.∞.3.∞ | |||||||||
(∞ 8 8) |
t0(∞,8,8) (∞.8)8 |
h0(∞,8,8) (16.∞.16.4)8 |
t01(∞,8,8) (8.∞)2 |
h01(∞,8,8) (4.4.4.∞)2 |
t1(∞,8,8) (8.∞)8 |
h1(∞,8,8) (16.4.16.∞)8 |
t12(∞,8,8) 8.16.∞.16 |
h12(∞,8,8) 4.4.4.8.4.∞.4.8 |
t2(∞,8,8) 8∞ |
h2(∞,8,8) (∞.4)∞ |
t02(∞,8,8) 8.16.∞.16 |
h02(∞,8,8) 4.4.4.8.4.∞.4.8 |
t012(∞,8,8) 16.16.∞ |
s(∞,8,8) 3.8.3.8.3.∞ | |||||
(∞ ∞ 8) |
t0(∞,∞,8) (∞.8)∞ |
h0(∞,∞,8) (∞.∞.∞.4)∞ |
t01(∞,∞,8) 8.∞.∞.∞ |
h01(∞,∞,8) 4.4.4.∞.4.∞.4.∞ |
t1(∞,∞,8) ∞16 |
h1(∞,∞,8) (16.∞)16 |
t12(∞,∞,8) 8.∞.∞.∞ |
h12(∞,∞,8) 4.4.4.∞.4.∞.4.∞ |
t2(∞,∞,8) (∞.8)∞ |
h2(∞,∞,8) (∞.∞.∞.4)∞ |
t02(∞,∞,8) (∞.16)2 |
h02(∞,∞,8) (4.∞.4.8)2 |
t012(∞,∞,8) 16.∞.∞ |
s(∞,∞,8) 3.8.3.∞.3.∞ | |||||
(∞ ∞ ∞) |
t0(∞,∞,∞) ∞∞ |
h0(∞,∞,∞) (∞.∞)∞ |
t01(∞,∞,∞) (∞.∞)2 |
h01(∞,∞,∞) (4.∞.4.∞)2 |
t1(∞,∞,∞) ∞∞ |
h1(∞,∞,∞) (∞.∞)∞ |
t12(∞,∞,∞) (∞.∞)2 |
h12(∞,∞,∞) (4.∞.4.∞)2 |
t2(∞,∞,∞) ∞∞ |
h2(∞,∞,∞) (∞.∞)∞ |
t02(∞,∞,∞) (∞.∞)2 |
h02(∞,∞,∞) (4.∞.4.∞)2 |
t012(∞,∞,∞) ∞3 |
s(∞,∞,∞) (3.∞)3 |
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